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PreprintarXiv licencearXiv

Conformal boundary rigidity for simple Finsler metrics

  • Kelvin Lam
  • Hanming Zhou
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Abstract

In this paper we prove that simple Finsler manifolds are conformally stable. Given a simple Finsler manifold and a class of conformal factors, we characterize the singularity of their induced boundary distance functions which allows us to define an appropiate H2 norm. We then obtain a stability estimate with respect to this Sobolev norm and the L2 norm on the class of the conformal factors. To prove the main theorems, we adapt the classical integration by parts technique employed by Mukhometov \cite{Muhometov} to the Finsler setting.

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Cite

BibTeXRIS
BibTeX
@misc{lam2026conformal,
  title = {{Conformal boundary rigidity for simple Finsler metrics}},
  author = {Kelvin Lam and Hanming Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09527},
  eprint = {2609.09527},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09527},
}
RIS
TY  - UNPB
TI  - Conformal boundary rigidity for simple Finsler metrics
AU  - Kelvin Lam
AU  - Hanming Zhou
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09527
UR  - https://arxiv.org/abs/2609.09527
AB  - In this paper we prove that simple Finsler manifolds are conformally stable. Given a simple Finsler manifold and a class of conformal factors, we characterize the singularity of their induced boundary distance functions which allows us to define an appropiate H^2 norm. We then obtain a stability estimate with respect to this Sobolev norm and the L^2 norm on the class of the conformal factors. To prove the main theorems, we adapt the classical integration by parts technique employed by Mukhometov \cite{Muhometov} to the Finsler setting.
ER  -